The Physics of Punkin Chunkin

It is pumpkin throwing time (officially, it is Punkin Chunkin). I rather enjoy this show on the Discovery channel. And this year it will be hosted by the MythBusters – Adam and Jamie. I must like this stuff because of the building aspect. It most likely is not because of the science content. Unfortunately, last year’s episode had some problems. Let me just go ahead and list my past pumpkin launching posts (note that the event is intentionally called ‘punkin chunkin’).

Punkin Chunkin circular motion mistake. Here is an example of the centrifugal force launchers explanation. They make the classic mistake (next to getting involved in a land war in Asia) of thinking the pumpkin will fly off in a direction directly away from the circle. In fact, it will fly off in a direction tangent to the circular motion.

Will the chunkers every make the mile range mark? In short, they would need to launch the pumpkins at about 1000 mph to get that far. Most current launchers (or at least the ones from 2008) shoot them at about 600 mph. The problem with increasing the launch speed is that you increase the acceleration of the pumpkin to the point where it breaks (unless you have a super-long launch tube).

More on the centrifugal force launchers. Besides having a dumb name, these launchers put the pumpkins under very large accelerations before launch. This again leads to the problem of pumpkin survival.

The online Discovery site has some videos explaining the different pumpkin launchers, but it is a little light on the science. Can we add a little sprinkling of physics on top of this? I think so. Here is the simplest physics explanation that I can come up with for the three types of machines in the contest.

Pneumatic air cannons

Flickr photo by autiscy

If you have ever built a potato gun (and if you haven’t, you should) then you know about pneumatic air cannons. This group of punkin chunkers just puts a pumpkin in a tube with a valve separating it and a large tank of air at high pressure. When the valve is opened, all the air pushes the pumpkin out the tube and WOOSH! Off it goes.

What are the main physics ideas for this device? Work-energy. The work-energy principle basically says that the work done on an object is equal to its change in energy. What is work? Work is essentially a force applied over some distance. If the force and the direction of motion are the same way, then:

Where Δr is the displacement. For a pneumatic cannon, the force is from the air and the displacement is the length of the launching tube. The change in energy for the object (which would be the pumpkin in this case) would be kinetic energy. This means that:

So you want your pumpkin to go faster? Get a longer tube or put your air tank at a higher pressure (which would increase Fair). But there is one problem. Suppose you pump up your tank to something crazy, like 10,000 psi. Sure, this would give you are large force. However, it would also make the pumpkin have a large acceleration. Since the force of the air pushes on one side of the pumpkin and not the other, a large acceleration can smash the pumpkin inside the tube. This is bad. To prevent this, you would need a smaller force over a larger tube distance. Length of the tube is the key.

Trebuchets

There are actually several categories in the Punkin Chunkin that deal with things like a trebuchet (catapult – which is different). But let me just talk about a trebuchet. The basic idea is to hurl an object by using a change in gravitational potential energy. Here is a very basic diagram.

This also uses the work-energy principle. With the pneumatic cannon, I used just the pumpkin as the system. For the trebuchet, let me consider the machine and the pumpkin and the Earth as the system. This means that there will be some gravitational potential energy, but there will be no forces doing work on the system. If I look at the key parts of the system as the weight (the big block on the end) and the pumpkin, then I can write:

So, the weight decreases in potential energy and increases in kinetic energy. The pumpkin increases in both kinetic and potential. Since the weight has a much larger mass and is on a shorter “stick”, it’s decrease in potential can make the pumpkin have a large velocity.

But wait! There is more. Why do some trebuchets have wheels? Well, in the above picture, the counter weight will still have some kinetic energy. Wouldn’t it be nice if more of that energy went to the pumpkin? If you put the thing on wheels, as the counter weight falls the trebuchet moves in the direction of throwing (in order to conserve horizontal momentum). The result is that the weight mostly just moves down instead of down and sideways. Since the counter weight has less kinetic energy than the same thing without wheels, the pumpkin will gain more kinetic energy.

Centrifugal Machines

These machines are just like a rock-sling weapon. Is that what those are called? You know where you put the stone in a little pouch on a string and swing it around? Same thing here except that the pumpkin is at the end of some long arm. The arm spins until it reaches some pre-determined launch speed and the pumpkin is released.

In terms of how this works, at the very basic level it is just like the pneumatic cannons. The cannons speed up the pumpkin over some distance. The centrifugal machines do the same, but they increase the distance over which the acceleration happens by making it move in a circle first. So, there is nothing special about the circular motion except that it gives the pumpkin a longer amount of time to speed up.

I just thought that was an interesting comparison. But back to the physics. There are two important things with these centrifugal machines. If you want to accelerate the pumpkin by making it move in a circle, this also is an acceleration. Really, velocity and acceleration are vectors with the average acceleration defined as:

If you change the velocity vector of some object, it will have an acceleration. So, just making an object turn will mean it is accelerating. For an object that is only turning (moving in a circle at a constant speed), the magnitude of this acceleration is:

If you want more details about where this equation comes from – check this out. But the point is that if you are moving in a circle, you are accelerating. Really, this is why they machines will not likely shoot a pumpkin further than a pneumatic cannon. If you want to keep a low enough acceleration to prevent the pumpkin from getting squashed, you need a ginourmous arm length.

The other thing that comes up with centrifugal machines is the release point. In fact, this is a classic physics question (it shows up in lots of places). If I have a pumpkin moving around in a circle and I release it at the point shown, what path will the pumpkin take?

Which do you choose? Actually, this is a fun question to ask your friends and family. For some reason, choice “c” is popular. I guess this comes from a couple of ideas. First, the idea that there is some force pushing you that way (this is just a fake force that we make so that the rotating frame behaves like we would expect a non-rotating frame). Second, many people think that objects move in the direction of a force. This isn’t quite true. Objects change velocity in the direction of the force.

The correct answer above is “a”. Here are two shots from the 2008 Punkin Chunkin show. In these shots the narrator is trying to explain why a 30 degree launch angle is best. However, they show the release point, not the launch angle.